Linking cell fractured fragments together with Rigid Body Constraints set as 'breakable'
Why is it exploding?

The model explodes, because the game engine (BGE) detects an impulse from all objects against other and so every body is repelled. The impulses are calculated by BGE because the intersection of of all parts' collision bounds at the start point (here: frame 40) is interpreted as an impact. Read more about collision detection

What's the solution?

Use a larger margin at the cell fracture options 
Additionally choosing the right collision shape might also help. In most cases Convex hull is just fine.